# solving system of eqns: 4x+4y=4, -3x+5y=-51

#### todd5821

##### New member
Here is the problem: 4x + 4y = 4
-3x + 5y = -51

I have tried multiplying, and substitution and I can't figure out how to get the correct answers.

Here is what I have done so far:

3(4x + 4y=4) 12x + 12y = 12
4(3x - 5y = 51) 12x - 20y = 204
-8y = 216
y = 27

I know that that's not right, but I don't know what I did wrong!

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: solving equations

todd5821 said:
Here is the problem: 4x + 4y = 4
-3x + 5y = -51

I have tried multiplying, and substitution and I can't figure out how to get the correct answers.

Here is what I have done so far:

3(4x + 4y=4) 12x + 12y = 12
4(3x - 5y = 51) 12x - 20y = 204
-8y = 216 32y = -192 --> y = -6
y = 27

I know that that's not right, but I don't know what I did wrong!

#### Mrspi

##### Senior Member
Re: solving equations

todd5821 said:
Here is the problem: 4x + 4y = 4
-3x + 5y = -51

I have tried multiplying, and substitution and I can't figure out how to get the correct answers.

Here is what I have done so far:

3(4x + 4y=4) 12x + 12y = 12
4(3x - 5y = 51) 12x - 20y = 204
-8y = 216
y = 27

I know that that's not right, but I don't know what I did wrong!
Your error is in the subtraction. 12x - 12x is 0x. 12y - (-20y) is 12y + 20y, or 32y. 12 - 204 is -192. So, you should have

32y = -192

Personally, I find it easier to eliminate one of the variables by ADDING rather than subtracting (since errors can easily occur when subtracting negatives).

Multiply the first equation by 3, and the second by -4.

12x + 12y = 12
-12x + 20y = -204

Now, add the two equations together......